Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2022-07-04 , DOI: 10.1016/j.aml.2022.108299 Lucio Boccardo , J. Ignacio Tello
In this article we study the existence of solutions of a system of partial differential equations of elliptic type, describing the distribution of a biological species “” and the density of a chemical stimulus “” in a bounded domain of . The equation for includes a chemotaxis term with nonlinear flux limitation which depends on the exponent .
The equation for is given by where presents a subcritical production term and satisfies the equation The matrix of coefficients, , is a known, symmetric and positive defined with coefficients is a given real constant, is a non-negative function belonging to , . The production term exponent, , is assumed to be positive and fulfills one of the following constrains or for .
The problem is completed with Dirichlet boundary conditions for and . The main result of the article includes the existence of positive solutions in
中文翻译:
在具有通量限制和亚临界信号产生的椭圆趋化系统上
在本文中,我们研究了椭圆型偏微分方程组解的存在性,描述了生物物种的分布“” 和化学刺激的密度 “” 在有界域中的. 方程为包括具有非线性通量限制的趋化性项,其取决于指数.
方程为是(谁)给的在哪里提出了一个亚临界生产术语并满足方程系数矩阵,, 是一个已知的、对称的和正定义的系数 是给定的实常数,是一个非负函数,属于,. 生产项指数,, 被假定为正并满足以下约束之一或者为了.
问题用狄利克雷边界条件完成和. 本文的主要结果包括存在正解